graphicscard64
Answered

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Use the properties of exponents to determine the value of aa for the equation:
[tex]\frac{\sqrt[3]{4} }{x} =x^{a}[/tex]

Sagot :

Answer:  a = -2/3

Step-by-step explanation:

Let's start by multiplying both sides by [tex]x[/tex] to simplify:

[tex]$4^{1/3} = x^a \times x$[/tex]

[tex]$4^{1/3} = \underbrace{x \times x \times x \times \cdots \times x}_{a\ \textrm{times}} \times \,x$[/tex]

[tex]$4^{1/3} = \underbrace{x \times x \times x \times \cdots \times x \times x}_{a+1\ \textrm{times}}$[/tex]

[tex]4^{1/3} = x^{a+1}[/tex]

Looking only at the exponents, it seems like [tex]1/3 = a+1[/tex], so [tex]a = \boxed{-2/3}[/tex].

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